Police chiefs have been accused of misunderstanding a cross-party effort to fight anti-Muslim prejudice after they publicly warned it risked undermining the fight against terrorism and hampering free speech.

The row centres on a proposed new definition of Islamophobia by a group of parliamentarians who say they consulted extensively before writing it, including with some police officers.

The definition from the all-party parliamentary group on British Muslims is: “Islamophobia is rooted in racism and is a type of racism that targets expressions of Muslimness or perceived Muslimness.”

The National Police Chiefs Council, which represents the leaders of law enforcement in England and Wales, issued a statement voicing their concerns on Tuesday night. Its chair, Martin Hewitt, said: “We take all reports of hate crime very seriously and will investigate them thoroughly. However, we have some concerns about the proposed definition of Islamophobia made by the all-party parliamentary group on British Muslims.

“We are concerned that the definition is too broad as currently drafted, could cause confusion for officers enforcing it and could be used to challenge legitimate free speech on the historical or theological actions of Islamic states. There is also a risk it could also undermine counter-terrorism powers, which seek to tackle extremism or prevent terrorism.

“It is important that any definition of anti-Muslim hostility is widely consulted on and has support across the Muslim community.”

One case study from the parliamentarians’ report into Islamophobia suggests the definition was drawn up in part to tackle possible police prejudice.

The anonymous respondent said: “I was stopped at Heathrow airport. The policeman said that they targeted me because of my attire. This has happened to me so many times. I cannot report it because the police do not see this as Islamophobic behaviour.”

Some critics of the definition claim it risks threatening free speech. However, Harun Khan, the secretary general of the Muslim Council of Britain, said police had misunderstood the proposed definition.

He said: “Mr Hewitt is reported to be of the belief that anti-terrorist operations would be hampered if the proposed definition of Islamophobia is adopted. If true, such a view belies a woeful misunderstanding of the proposed definition. We find it quite extraordinary that such a public intervention is made without even engaging with those involved in the definition.

“Our understanding is that the police and security forces will rightly fight terrorism based on intelligence and a scrutiny of the evidence. Anti-terrorist operations can only be ‘hampered’ if counter-terror officers have been targeting Muslims because of their identity (or Muslimness as the definition states), categorising them as security concerns. If this is the case, it confirms long-voiced concerns about the disproportionate focus and impact of counter-terror operations on Muslim communities.

“We would urge Mr Hewitt to carefully reflect on whether, in a climate where there are concerns of discrimination, it is sensible to publicly intervene in this way.”

The report that came up with the definition found Muslims facing higher levels of hate crime, with official figures showing that the risk of being a victim of race hate crime was highest for Muslim adults (1.7%) compared with, for example, 0.2% for Christian adults.